Published by Associazione Teriologica Italiana Volume 28 (2): 202–207, 2017

Hystrix, the Italian Journal of Mammalogy

Available online at:

http://www.italian-journal-of-mammalogy.it doi:10.4404/hystrix–28.1-12299

Research Article

EBHS in European brown hares (Lepus europaeus): disease dynamics and control

Monica Salvioli1, Sara Pasquali2, Antonio Lavazza1, Mariagrazia Zanoni1, Vittorio Guberti3, Mario Chiari1,∗, Gianni Gilioli4

1Istituto Zooprofilattico Sperimentale della Lombardia ed Emilia Romagna, Via Bianchi 7/9, 25124 Brescia, Italy2CNR-IMATI, via Bassini 15, 20133 Milano, Italy

3Istituto Superiore per la Protezione e la Ricerca Ambientale, Via Ca’ Fornacetta 9, 40064 Ozzano dell’Emilia, Bologna, Italy4DMMT, Università degli Studi di Brescia, viale Europa 11, 25123 Brescia, Italy

Keywords:European Brown Hare Syndromebrown hareSIR modelpopulation dynamics

Article history:Received: 23 December 2016Accepted: 26 May 2017

AcknowledgementsThe authors gratefully acknowledge the local hunters (Ambito Territorialedi Caccia Unico di Brescia, Brescia Province, Northern Italy); withouttheir cooperation, the validation of this study would not have beenpossible. The authors wish to thank Dr. Lesley Benyon (ScienceDocs)for the editing of this manuscript.

Abstract

Brown hares have undergone a substantial population decline in Europe during recent decades,caused by, among other factors, the occurrence of European Brown Hare Syndrome (EBHS). Toimprove our knowledge regarding EBHS epidemiology, we developed a mathematical model thattakes into consideration both brown hare biology and the infection dynamics of the EBHS virus(EBHSV). The model consists of eight ordinary differential equations simulating the spread of thevirus in a closed hare population. Simulations showed that EBHSV’s transmission has complexdynamics, which are strongly affected by the hare density. In particular, a density threshold of 7individuals/km2 was identified, determining two opposite epidemiological patterns: the extinctionof the EBHSV below the threshold and its endemic stability when the hare population density isabove the threshold, with a seroprevalence proportional to the population density. The model wasvalidated using serological data collected in different areas in the province of Brescia (NorthernItaly). The results suggested that the maintenance of the endemic circulating viral level throughdensity control mechanisms is the best strategy for reducing EBHS’s impact.

IntroductionEuropean brown hare (Lepus europaeus) is an important game speciesthat is subjected to specific hunting management and restocking pro-grams. In the last decades, a progressive decline in the hare popula-tion has occurred in Italy, as well as in the rest of Europe (Edwardset al., 2000). One major cause of this decline is the occurrence ofEuropean BrownHare Syndrome (EBHS), a highly contagious disease,that emerged in the ’80s and is now considered endemic in all Europeancountries (Duff and Gavier-Widén, 2012). EBHS can be transmittedby direct contact with infected animals, or indirectly through infec-ted materials or equipment used during capture operations, because ofthe high environmental resistance of the causal virus (EBHSV). AnEBHSV infection can achieve almost 100% morbidity when the virusis introduced into a naive brown hare population, and the induced mor-tality is age-dependent and varies from 40 to 70% (Cammi et al., 2003;Duff and Gavier-Widén, 2012). The disease has not been observedin hares younger than 2–3 months of age, because if they come intocontact with the virus, the resulting infection leads to the developmentof lifelong immunity, without the exhibition of any clinical symptoms(Zanni et al., 1993; Lavazza et al., 1997).Targeted EBHS surveillance is commonly based on the assessment

of the immunological status of the population using serological determ-ination of anti-EBHSV titres (Paci et al., 2011). On the basis of surveydata, Lavazza et al. (1997) hypothesized that the spread and circula-tion of EBHSV are linked to the hare’s population density. In particu-lar, they considered the presence of a density threshold, between 8 and15 hares/km2, that determines which of two opposite scenarios occurs.One scenario is characterized by a low EBHSV circulation (i.e. a highnumber of seronegative hares) below the threshold, and the other by a

∗Corresponding authorEmail address: mario.chiari@izsler.it (Mario Chiari)

high EBHSV prevalence (i.e. high number of seropositive hares) abovethe threshold.

To explore the heterogeneity involved in these field observations, therole of population abundance in the epidemiological pattern of EBHSshould be investigated using an appropriate epidemiological modellingapproach. Because of the importance of the host age in viral transmis-sion and occurrence of disease outbreaks, as well as the age relatedcontact rate of the host, elements of the population ecology of the spe-cies, such as host’s social behaviour and dimensions of the home range,should be included in the model. This results in the consideration of aneco-epidemiological model of EBHS dynamics.

Dynamical models inspired by an eco-epidemiological approachhave been proposed to investigate the transmission of infectious wild-life disease-causing agents, focusing in particular on those that have azoonotic impact (Iwami et al., 2007), can be transmitted to livestock(Keeling, 2005; Gilioli et al., 2009) or threaten endangered wildlifepopulations (White et al., 2014). For example, models involving wild-life infections include rabies in fox (Anderson et al., 1981), sarcopticmange among chamois (Lunelli, 2010), and tuberculosis in badgers(Anderson and Trewhella, 1985; Cox et al., 2005) and white-tailed deer(McCarty and Miller, 1998).

To the best of our knowledge, there are no published models describ-ing the relationship between the disease prevalence and the populationabundance for the EBHS. The lack of modelling tools and the need toaccount for the ecology of the host in the disease dynamics motivatedthe model-based exploration of the dependence of epidemiological pat-terns on the hare’s population abundance.

Hystrix, the Italian Journal of Mammalogy ISSN 1825-5272 9th November 2017©cbe2017 Associazione Teriologica Italianadoi:10.4404/hystrix–28.1-12299

EBHS dynamics and control

MethodsModel descriptionTo simulate the eco-epidemiology of EBHS in a closed age-structuredhare population, we developed a compartmental model, combiningdemographic and disease transmission processes.The demographic structure of the hare population is based on three

age classes: newborn (N), younger than 3 months, young (Y ), from 3 to6 months, and adult (A), older than 6 months. A density-dependence inhare demography is assumed to take place on host fecundity, whereasno evidence of relation between hare density andmortality/survival ratewere described (Frylestam, 1979;Marboutin et al., 2003; Schmidt et al.,2004). Demographic processes, including development, mortality andfecundity, are represented by fluxes in the diagram in Fig. 1.The number of individuals in the three classes changes due to demo-

graphic processes, including development and mortality. Moreover,adults reproduce, contributing to the renewal of the newborn class.The EBHSV infection process changes the status of the individuals

from susceptible to infected and infectious, and finally to immune or re-covered. Tomodel the infection dynamics, individuals in each age classwere further classified into three categories: susceptible (S), infectedand infectious (I) and recovered/immunised/immune (R). Since haresyounger than 2–3 months of age do not develop symptoms or die fromEBHS, the class of the infected/infectious newborn hares was omitted.Newborn hares are considered to be susceptible (NS) after birth, at leastafter the disappearance of maternal immunity, and when they come intocontact with the virus they pass to the recovered class (NR). Those new-born hares not exposed to the virus within three months develop intosusceptible young hares (YS) and then, after three months, into suscept-ible adults (AS). Susceptible individuals that come into contact withinfected and infectious individuals, either young or adult, also becomeinfected and infectious (YI or AI respectively). They can either die fromEBHS at a stage-specific mortality rate ki (i =Y,A) or recover at a rater and join the recovered class (YR or AR, respectively). Recovered haresdo not contribute to the transmission of the virus and remain immuneto further infections. Since the infection from EBHSV has typically ashort clinical course, hares spend proportionally little time in the infec-ted class: for this reason the demographic processes (natural mortality,

Figure 1 – The compartmental model, combining both demographic and EBHS epidemi-ological processes. The demographic structure of the hare population is composed ofthree age classes: newborn (N), younger than 3 months, young (Y ), 3–6 months, and adult(A), older than 6 months. Demographic processes, including development, survival andfecundity, are represented by vertical fluxes in the diagram. In the figure f , representedthe maximum fecundity; dN = dY , the development rate (newborn and young); mA = mY ,the natural mortality (young and adult); mN , the natural mortality (newborn); r, the recov-ery rate; iN , the maximum infection rate for newborn hares; µN , the density dependenceinfection parameter (newborn); iY , the maximum infection rate for young hares; µY , thedensity dependence infection parameter (young); iA ,the maximum infection rate for adulthares; µA , the density dependence infection parameter (adult); kY , the EBHS-induced mor-tality (young); kA , the EBHS-induced mortality (adult) and K, the carrying capacity of theenvironment.

development and reproduction) involving infected hares (both youngand adult) were assumed to be negligible and were not considered inthe model. The population dynamics and disease processes illustratedabove can be described by the following system of eight ordinary differ-ential equations (ODEs), in which the variables are expressed in termsof the number of animals per unit area:

dNS

dt= f

(1− AS +AR

K

)(AS +AR)− iN

(1− e−µN(YI+AI)

)NS+

−dNNS−mNNS(1)

dYS

dt= dNNS− iY

(1− e−µY (YI+AI)

)YS−dYYS−mYYS (2)

dAS

dt= dYYS− iA

(1− e−µA(YI+AI)

)AS−mAAS (3)

dYI

dt= iY

(1− e−µY (YI+AI)

)YS− (kY + r)YI (4)

dAI

dt= iA

(1− e−µA(YI+AI)

)AS− (kA + r)AI (5)

dNR

dt= iN

(1− e−µN(YI+AI)

)NS−dNNR−mNNR (6)

dYR

dt= dNNR + rYI −dYYR−mYYR (7)

dAR

dt= dYYR + rAI −mAAR , (8)

where: f , maximum fecundity; dN = dY , development rate (newbornand young); mA = mY , natural mortality (young and adult); mN , naturalmortality (newborn); r, recovery rate; iN , maximum infection rate fornewborn hares; µN , density dependent infection parameter (newborn);iY , maximum infection rate for young hares; µY , density dependent in-fection parameter (young); iA, maximum infection rate for adult hares;µA, density dependent infection parameter (adult); kY , EBHS-inducedmortality (young); kA, EBHS-induced mortality (adult); K, carryingcapacity of the environment.

Model parameter definitions and estimationsThe model parameters were taken from published literature regardingthe biological characteristics of the European hare, except for the twoparameters involved in the transmission process, i an µ , which werecalibrated using field data. All of the parameters, together with theirdefinitions and values, are listed in Tab. 1.

Demographic parameters include development, mortality and re-cruitment rates. Development depends on the stage-specific develop-ment rates dN and dY , which describe the rate of individuals transferredfrom N toY classes and fromY to A classes, respectively. Developmentrates were estimated to be equal to 1

90days−1 in our model because, ac-

cording to the biological data, hares are supposed to spend 3months (90days) in both the N and Y classes (Trocchi and Riga, 2005). Mortalityis described by a linear function with age-specific mortality rates. Mor-tality rates (0.0022 days−1 for young and adult hares and 0.0033 days−1

for newborn hares) were derived from the mortality statistics reportedby Trocchi and Riga (2005).

The recruitment is described by a density-dependent fecundity ratefunction, in which themaximum fecundity rate f , which corresponds toan average of 13 leverets per female per year (Trocchi, personal data,Bologna 2010–2015), is multiplied by the term

(1− AS+AR

K

), which

depends on the carrying capacity K. This carrying capacity-dependentcomponent that appears in the fecundity rate function was chosen tosimulate the decrease in fecundity that occurs once a population is closeto K.

Disease-specific parameters include the infection and the recoveryrates, as well as the disease-induced mortality. The recovery rater = 1

3days−1 was estimated from Frölich and Lavazza (2008), who re-

ported 72 h as the average duration of infection. EBHS-induced mor-tality rates, 0.2 days−1 for adult hares and 0.46 days−1 for young hares,were estimated from survey data by Cammi et al. (2003).

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Table 1 – Hare demographics and EBHSV infection parameters in the transmission model. Parameters were estimated from published literature on the European hare or calibrated usingfield data.

Parameter Description Value References

f Maximum fecundity 13 (leverets/female)/year Trocchi, personal data Bologna 2010–2015dN = dY Development rate (newborn and young) (1/90) / days Frölich and Lavazza (2008); Trocchi and Riga (2005)mA = mY Natural mortality (young and adult) 0.0022 / days Trocchi and Riga (2005)

mN Natural mortality (newborn) 0.0033 / days Trocchi and Riga (2005)r Recovery rate (1/3) / days Frölich and Lavazza (2008)iN Maximum infection rate for newborn hares 0.3040 / days CalibrationµN Density dependent infection parameter (newborn) 1.0507 / (hares/km2) CalibrationiY Maximum infection rate for young hares 0.3040 / days CalibrationµY Density dependent infection parameter (young) 1.0507 / (hares/km2) CalibrationiA Maximum infection rate for adult hares 0.3040 / days CalibrationµA Density dependent infection parameter (adult) 0.2139 / (hares/km2) CalibrationkY EBHS-induced mortality (young) 0.46 / days Cammi et al. (2003)kA EBHS-induced mortality (adult) 0.2 / days Cammi et al. (2003)K Carrying capacity of the environment 56 K 6100 hares/km2 Trocchi and Riga (2005)

Model calibration

A calibration process based on a least squares method was used to es-timate the parameters involved in the infective agent’s transmission pro-cess. The infection process is described by a monotonically increas-ing, convex and uniformly bounded function, following the Ivlev func-tional response (Ivlev, 1961). The Ivlev functional response, a non-linear density-dependent function, is a simple function derived fromprey-predator models and describing the outcome of a search/contactprocess. This function has two positive parameters: ik (k = N,Y,A),which represents the maximum infection rate and µk (k = N,Y,A),which regulates the relationship between disease transmission and haredensity. This non-linear density-dependent model of infection was in-troduced to account for the action of several density-related factors,such as the persistence of the virus in the environment, the host’s so-cial behaviour and the dimension of the home range, that play a rolein the disease transmission process (Pearce et al., 2006; Preedy et al.,2007).Since there is no evidence of an influence of age on the infection

rate, the value of the parameter ik, representing the susceptibility to theinfection, was assumed to be the same for all the ages.As for the density, both newborn and young hares seem to be partic-

ularly sensitive, because they tend to stay in the familiar group homerange until they reach sexual maturity. On the contrary, because oftheir solitary habits, adult hares seem to be less sensitive to density-dependent EBHSV-associated factors. Therefore, an increase in popu-lation density is more likely to affect the average contact rates of new-born and young animals rather than that of adults. Thus, the parameterµk for newborn and young hares was assumed to be equal and higherthan that of the adults. Both i and µk were estimated using the modeland published biological data obtained from field surveys (Paci et al.,2011; Chiari et al., 2014).Simulation results were compared with serological data, collec-

ted from free-ranging hares captured for restocking reasons betweenDecember and January over seven consecutive years (2006–2013), thatestimated the disease prevalence. The samples were collected in sevenprotected, but open, “breeding for restocking” grounds (BfRGs) in theprovince of Brescia (Northern Italy) characterized by different densityvalues. Chiari et al. (2014) reported that in areas with density val-ues higher than 15 hares/km2 the recovered fraction was greater than60% during six out of seven surveyed years. The calibration proced-ure was based on data derived from the BfRG in Quinzano becausea constant brown hare density was reported in this BfRG over a longsurvey period. The set of parameters found to minimize the distancebetween the model output and the field data in the sense of least squareswas: i=0.3040 (95% CI: 0.2947–0.3133); µN = µY=1.0507 (95% CI:0.9952–1.1041); µA=0.2139 (95% CI: 0.205–0.2230). Figure 2 showsthe model fitting field data used to estimate the infection parameters.

Sensitivity analysisThe aim of the sensitivity analysis was to describe how an infinites-imal change in the model parameters could affect the output variables.The sensitivity estimation was performed as described by Keeling andGilligan (2000):

S = limP→P0

log(

V (P)V (P0)

)log

(PP0

) =P0

V (P0)

∂V∂P

, (9)

where S represents the sensitivity with respect to the parameter P(whose default value is P0) and V represents the model output. In thepresent work the fraction of AR represents the output variable, and thesensitivity of the model was explored with respect to the K and theparameters involved in the infection transmission, i and µk.

SimulationsSimulations were run to investigate the hare population and the diseasedynamics. The equations (1–8) were numerically solved using MatlabODE solvers (Release 2014a).

Population dynamics in the absence of infection were investigated byrunning simulations over a period of 10 years. The initial condition ofthe population was supposed to be half K, which varies in the range of5–100 hares/km2, with an initial age ratio of N+Y

A =1.5, being close tothe 1.53 value reported by Trocchi and Riga (2005). Infection dynamics

Figure 2 – Result of the fitting procedure used to estimate the infection parameters i andµN = µY and µA .

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EBHS dynamics and control

Figure 3 – Time evolution of the hare population model without infection (YI = AI = 0) at carrying capacity (K) values of 5, 10 and 50 hares/km2 .

were simulated over the same time period and within the same rangeof K. Initial conditions were chosen as above, but one adult hare wasassumed to be infectious at day zero. In both simulations a total of 60%of adult hares were removed yearly from the population to simulate theregular hare translocation (i.e., captured in protected areas, transportedand released in public hunting areas), which takes place every winterin each BfRG.

Basic reproduction numberThe basic reproduction number R0 is a key concept in epidemiologyand in the study of infection dynamics. It is defined as the expectednumber of secondary infections arising from a single infectious indi-vidual in a completely susceptible population; for this reason, it is com-monly used as a threshold parameter that predicts whether an infectionwill spread. In particular, whenR0>1 the infection is expected to invadethe susceptible population, whereas if R0<1 the infection will probablydie out in the long run. There are several common methods of formu-lating R0 as well as means of estimating its value from epidemiologicaldata. Following Heffernan et al. (2005), R0 was estimated at differentdensity values from the final fraction of susceptibles S(∞):

R0 =logS(∞)

S(∞)−1. (10)

Such an approach is appropriate for any model with a closed popu-lation, where the infection leads either to immunity or death, as in thecase of EBHS (Heffernan et al., 2005).

ResultsBecause of the complexity of the system, the properties of the modelwere investigated from a numerical point of view only. Simulationswere run at different K values to investigate the presence of thresholdsthat determine regime shifts in the epidemiological pattern (from en-demic stability to disease extinction in local and isolated populations).

Population dynamicsPopulation dynamics were first investigated in the absence of infection(YI and AI=0) within aK range from 5 to 100 hares/km2. The time evol-ution of the model at three different K values (5, 10 and 50 hares/km2)is reported in Fig. 3.At 5 hares/km2, the system reached K within the first 2 years with an

age ratio N+YA =1.46 after the last sampling. At 10 and 50 hares/km2 the

equilibrium was reached within 2 years with an age ratio of 1.42 afterthe last sampling (Fig. 3). Density valuesmentioned in this section referto pre-breeding values and account for the three age-classes together,unless otherwise specified.

Epidemiological patternsEBHSV transmission dynamics were investigated for the sameK valuesthat had been evaluated in the disease-free dynamics. The dynamics of

the epidemiological system at the three selected K values are reportedin Fig. 4.

Since two distinct behaviours of the model at 5 and 10 hares/km2

were found, the intermediate values were carefully evaluated. Sim-ulations revealed that the system had a threshold-like behaviour. Inparticular, a density threshold of approximately 7 individuals/km2 thatseparated two opposite epidemiological patterns, the extinction of thedisease in the hare population below the threshold and the persistenceabove, was identified.

With a value of K of 5 hares/km2 at the equilibrium the whole pop-ulation was susceptible to the infection, and there were no infected orrecovered individuals. In this simulation, the virus underwent a rapidextinction.

However, above the carrying capacity threshold of7 individuals/km2, the fraction of infected hares was always differentfrom zero and the dynamics of the EBHSV infection progressively con-verged toward an endemic equilibrium. At a density of 10 hares/km2

the population was mostly susceptible at the end of simulated time ho-rizon, but a significant fraction of recovered (42%), and a small amountof infected individuals, were constantly present (Fig. 4).

When the K value was set at 50 hares/km2 the population was mostlyrecovered (89%).

Overall, the fraction of the population recovered at equilibrium waspositively related to K, ranging from 16% at a density value of 7hares/km2 to 95% at the highest density studied (100 hares/km2). Theexpected seroprevalence of young and adult hares as a function of K isreported in Fig. 5.

Sensitivity analysisK was determined to be the most sensitive parameter, as concluded byLavazza et al. (1997) (Tab. 2). Thus, small changes in this parameterproduce large variations in the AR fraction. It should be emphasizedthat in ourmodel hare populations tend to saturate the different carryingcapacity values. Different K values were tested to verify the effects onthe output variable (fraction recovered). In particular, the impacts ofsmall changes in the parameters on themodel’s behaviour were found tobe greater at low K values rather than at high values. The infection ratei and the parameters µN = µY and µA were found to be less sensitive.

Table 2 – Sensitivity analyses of the model parameters. The carrying capacity (K) was themost sensitive parameter. The infection rate i, and the parameters µN = µY and µA , werefound to be less sensitive.

Parameter Description Sensitivity

K Carrying capacity 35i Infection rate 0.5

µN = µY Density dependent infection parameter (new-born and young)

0.3

µA Density dependent infection parameter(adult)

0.25

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Hystrix, It. J. Mamm. (2017) 28(2): 202–207

Figure 4 – Time evolution of EBHSV transmission dynamics at carrying capacity (K) values of 5, 10 and 50 hares/km2 .

Basic reproduction numberThe basic reproduction number R0 was found to vary with the carryingcapacity K; in particular, its value was found to be approximately onearound the threshold of 7 hares/km2 and to increase above it.

Estimates of the basic reproduction number R0 for different carryingcapacity values are reported in Tab. 3.

Table 3 – Estimation of the basic reproduction number R0 at di�erent carrying capacityvalues.

Carrying capacity K Basic reproduction number R0

50 2.1520 1.6510 1.298 1.217 1.03

DiscussionWe investigated the impact of hare density on EBHSV infections withina wide density range (5–100 hares/km2), which was consistent with thebiological hare data estimated in Italy and Europe (Trocchi and Riga,2005). Our model focused on the role of population density becauseit was considered the main factor influencing EBHSV transmission(Lavazza et al., 1997).To analyse the impact of EBHS, population dynamics simulations

in the absence of the disease were first considered. Despite the per-centage of adult hares (60%) removed every year from the model tobetter simulate hare management in BfRGs, K was reached in all of thedisease-free scenarios investigated. The resulting age structure at equi-librium after the last sampling was always close to the natural age ratioreported in Italian and other European brown hare populations (Trocchiand Riga, 2005; Pepin, 1987).Further simulations that included the introduction of infected hares

into the original susceptible population were run to evaluate the con-

ditions for EBHS maintenance. The system was highly sensitive tovariations in the parameters of the infection function. In particular, theparameter µ was found to influence the relationship between the infec-tion probability and the hare density and, therefore, the pattern of theepidemics. This fact suggests that the transmission cannot be determ-ined only by random contact, but that more sophisticated mechanismsare involved. For example, the high resistance of EBHSV in the envir-onment (Frölich and Lavazza, 2008) might influence the transmissionof the disease. Moreover, the habit of sharing shelter and the dimensionof the home range may play a role in the transmission of EBHSV.

Lavazza et al. (1997) hypothesized the presence of a double-threshold behaviour: in areas where the hare density is lower than 8hares/km2 the virus transmission is reduced and irregular, while inareas where the density is greater than 15 animals/km2 the virus is en-demically maintained.

Our simulation outcomes suggested the presence of a singlethreshold of approximately 7 individuals/km2. When the density waslower than the threshold, the system had a disease-free equilibrium anda local extinction of the virus was reported (Fig. 4). This outcome cor-roborated field data, which indicated that at low density values the virusdies out in the short term (Paci et al., 2011; Chiari et al., 2014). As aconsequence of the absence of viral circulation, all of the animals rap-idly become susceptible to the infection, and the population is likelyto be exposed to recurrent EBHS outbreaks due to reintroductions ofthe virus. This has occurred in areas where the hare density is con-stantly below the threshold value (e.g. hunting areas in the north ofItaly) and all of the animals sampled were repeatedly seronegative (Paciet al., 2011; Chiari et al., 2014). EBHSV can be easily introduced intosuch hare populations because it can be transmitted directly by infec-ted animals and indirectly through infectedmaterials or passive vectors,such as predators (Frölich and Lavazza, 2008; Chiari et al., 2016). Ourmodel revealed this particular epidemiological situation, which allowsfor new epidemics, but the observed recurrent outbreaks due to the rein-troduction of the virus were not described. In fact, our model illustratesthe evolution of the disease in a closed population after a single intro-

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duction of the virus, whereas in the field the virus can be repeatedlyreintroduced into the population.When the hare density exceeded the value of 7 individuals/km2, the

virus was endemically maintained and constantly circulated in the pop-ulation due to the population’s renewal process that ensures a faster re-cruitment of newborn hares. In this scenario most individuals acquiredthe infection in early life and seroconverted before becoming suscept-ible to the disease, leading to an endemic equilibrium (Fig. 4). Thefraction of recovered/immune animals predicted by the model at differ-ent K values was consistent with the available field data. For instance,simulations showed a fraction of the 78% adult and young hares re-covered at a density of 25 individuals/km2, which was similar to fielddata that reported an average of 75% recovered in high-density areasduring the annual capture operation (Paci et al., 2011; Chiari et al.,2014).The simulated seroprevalence of young and adult hares as a function

of K is reported in Fig. 5.When comparing field values reported by Chiari et al. (2014) with

simulated seroprevalence values, the former resulted in a higher sero-prevalence value than the latter at the same carrying capacity K. Inaddition, in few cases a BfRG reported a density value higher than 7hares/km2 and a seroprevalence lower than the one predicted by themodel (Fig. 5). It should be emphasized that in the model the sero-prevalence is described as a function of K, whereas field data usuallyrefer to hare density because K cannot be easily estimated in the field.This fact might explain possible discrepancies between simulation res-ults and field data, even when the density reported is likely much lowerthan the K of the BfRG. Thus, the field data were generally consistentwith the simulated seroprevalence.The analysis of the basic reproduction number (Tab. 3) further sup-

ports numerical results.R0 was found to be related to the carrying capacity, in particular its

value grows asK increases. Moreover, the critical value ofR0 coincidesapproximately with the critical density threshold of 7 hares/km2. Boththese facts are consistent with the supposed influence of the densityon the infection dynamics of EBHS and with the presence of the twoopposite scenarios described above.

ConclusionsThe model’s results suggested that the brown hare population densitydirectly influenced the transmission of EBHSV, which is a main causeof the hare decline in Europe (Duff and Gavier-Widén, 2012). Becausea density-dependent mechanism in EBHSV transmission was demon-strated and a threshold of 7 hares/km2 was estimated, hare manage-ment should promote this minimal density to minimize the impact ofEBHS. High density values (>20 hares/km2) are difficult to achieve,

Figure 5 – Comparison of field seroprevalence values reported by Chiari et al. (2014) withsimulated seroprevalence ones. The expected seroprevalence values of young and adulthares are reported as a function of the carrying capacity (K).

especially in hunting areas and where the K of the environment is lim-ited. However, our results, showing that the higher the hare densityvalue, the lower the susceptible fraction of the population, should betaken into consideration. Because the eradication of EBHS in a wildhare population is not feasible (Chiari et al., 2014), the only way to re-duce the disease impact is to maintain EBHSV in the hare populationthrough a high hare population density, thus avoiding recurrent diseaseoutbreaks.

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Associate Editor: N. Ferrari

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